Analog Signal Resonance in PCB InterconnectsBy ZM Peterson • Mar 31, 2019
Looking through the words from the experts on signal integrity in PCBs, most folks talk about signal integrity in high speed digital devices, but there are fewer discussions of signal integrity problems that can arise in analog devices.
Here, we're not just talking about crosstalk in mixed signal devices. Obviously, crosstalk between signal traces in a PCB is important for ensuring signal integrity, as well as between digital and analog signals in a mixed-signal device. However, there is a particular effect that arises in analog signal traces that is ignored in most technical blogs and application notes. This concerns resonance in analog signals in PCB transmission lines.
Ringing vs. Signal Resonance
This effect concerns analog signal resonances that can arise on analog signal traces due to signal reflection in an interconnect. In digital signals, this manifests itself as ringing, which appears as an underdamped signal superimposed in a digital signal. A severe ringing signal bouncing throughout a signal trace due to a large source/load impedance mismatch might cause involuntary switching in sensitive logic circuits, contributing to bit rate errors.
Ringing arises due to a natural oscillation at the RLC resonance frequency in the trace that forms the interconnect, although this depends on the length of the interconnect and the imepdance profile of the load. Remember that a digital signal essentially places a momentary impulse of voltage/current in the trace, effectively exciting a signal at the RLC resonance. Unless ringing is very intense, or unless it is extremely underdamped, the gate capacitance, input impedance, and the saturation level in a logic circuit are sufficient to prevent or suppress involuntary switching. The the rise time of the reflected signal and the amplitude of a ringing signal needs to be extremely large to cause involuntary switching.
With analog circuits, the source of analog signal resonance is the same as ringing: impedance mismatch along an interconnect. However, the resonance produced by these two effects is different. Ringing in a digital signal arises due to a voltage/current impulse in the interconnect as the digital signal reflects. This excited signal slowly decays over time as the digital signal drops back to zero. In contrast, analog signals are continuously driven by an oscillator rather than by momentary bursts of voltage/current.
When a load is not impedance matched to source/trace, an analog signal can reflect from the impedance discontinuity at the load and propagate back through the interconnect towards the source. The counter-propagating electromagnetic fields can form a standing wave due to superposition, just like standing waves that occur on a string. Effectively, the trace acts like a radiating antenna.
This effect is well-known to occur in via stubs in high frequency PCBs. Via stubs act like hanging wires and can radiate strongly at high frequencies. This problem is especially problematic in multilayer boards with high layer count, wherein a via used to pass between two neighboring layers leaves a solid stub that passes through the remaining layers. These problems with signal resonance are typically mitigated by back-drilling the stub during assembly.
The standing waves that form in the interconnect cause the trace to act as a strong radiator at a single frequency. The electromagnetic field emitted from an interconnect can couple noise into nearby traces and components. With RF circuits, it is already difficult to reduce coupling between parallel lines to less than -45 dB, and this only exacerbates the coupling problem.
Predicting Analog Signal Resonance
Experimentally, you can measure a resonance spectrum using an oscilloscope while sweeping the input signal frequency. Predicting the resonant frequencies for analog signals in a trace can be a somewhat complicated problem, depending on a number of factors.
First, it is important to note that standing waves arise when the length of the interconnect is some multiple of either a quarter (for one impedance matched end of the trace) or half wavelength (neither end impedance matched) of the analog signal. These exact multiples can be integers in certain situations, or they can be solutions to a transcendental equation. In general, the resonant frequencies are determined from a dispersion relation, which is derived by applying the boundary conditions in the system.
Experimentally measured analog resonances due to signal reflection in an interconnect.
For an analog signal on a trace connecting a source and load, consider an example where the source, load, and trace are all mismatched. In this case, signal reflection occurs at the source and load ends of the trace. The electric field in the trace depends on the oscillation frequency of the source, the effective dielectric constant of the trace, and electromagnetic dispersion in the trace and the surrounding dielectric. In a real system, dispersion in the substrate will be appreciable and will cause the effective dielectric constant to vary with frequency, thus complicating the solution.
The impedance of the trace itself is also a function of frequency. Most designers, design software companies, and even the IPC simply take the impedance to be a frequency-invariant value that only depends on the dimensions and dielectric constant of the substrate, without considering the parasitic capacitance and inductance that is inherent in the circuit. However, this defies all physical logic and is really only an approximation. To quote Douglas Brooks, "In the opinion of many designers, there are no impedance formulas that are now considered adequate." Polar Instruments offers a decent overview of the mathematical formulation for trace impedance.
Suppressing Analog Signal Resonance
The best way to suppress analog signal resonance is to ensure impedance matching throughout your board. This is best done when you use impedance controlled design in your PCBs. This ensures that your traces will have consistent impedance throughout your board (50 Ohms, or 100 Ohms for differential pairs), and you will only need to worry about impedance matching components to your trace impedance.
Impedance controlled design requires selecting the appropriate trace geometry and arrangement to use throughout the board in order to guarantee impedance matching within the limits defined by manufacturing tolerances. A designer with the right software can specify matching constraints that ensure signal resonance does not cause major problems in your analog or mixed signal board.
In a future article, we'll examine the analytical solution to this problem for an analog and a digital signal reflecting at an impedance discontinuity. In short, this requires solving the wave equation for an electromagnetic field in the presence of a current source in a one dimensional system. More on that in a later article.